{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 500, Loss: 0.0001266076578758657\n",
      "Epoch 1000, Loss: 6.490482337540016e-05\n",
      "Epoch 1500, Loss: 3.748390736291185e-05\n",
      "Epoch 2000, Loss: 1.8464799723005854e-05\n",
      "Epoch 2500, Loss: 7.731980076641776e-06\n",
      "Epoch 3000, Loss: 2.9069008178339573e-06\n",
      "Epoch 3500, Loss: 1.2448442703316687e-06\n",
      "Epoch 4000, Loss: 7.845710001674888e-07\n",
      "Epoch 4500, Loss: 6.144564963506127e-07\n",
      "Epoch 5000, Loss: 4.806768174603349e-07\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.optim as optim\n",
    "\n",
    "# Define the neural network\n",
    "class Net(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(Net, self).__init__()\n",
    "        self.hidden1 = nn.Linear(1, 20)\n",
    "        self.hidden2 = nn.Linear(20, 20)\n",
    "        self.output = nn.Linear(20, 1)\n",
    "\n",
    "    def forward(self, x):\n",
    "        x = torch.tanh(self.hidden1(x))\n",
    "        x = torch.tanh(self.hidden2(x))\n",
    "        x = self.output(x)\n",
    "        return x\n",
    "\n",
    "# Define the source term f(x)\n",
    "def f(x):\n",
    "    return torch.sin(torch.pi * x)\n",
    "\n",
    "# Initialize the neural network\n",
    "net = Net()\n",
    "\n",
    "# Define the loss function\n",
    "def loss_function(x):\n",
    "    x = x.view(-1, 1)\n",
    "    x.requires_grad = True\n",
    "    N = net(x)\n",
    "    u = x * (1 - x) * N\n",
    "    u_x = torch.autograd.grad(u, x, grad_outputs=torch.ones_like(x), create_graph=True)[0]\n",
    "    u_xx = torch.autograd.grad(u_x, x, grad_outputs=torch.ones_like(x), create_graph=True)[0]\n",
    "    residual = u_xx + f(x)\n",
    "    return torch.mean(residual**2)\n",
    "\n",
    "# Training the neural network\n",
    "optimizer = optim.Adam(net.parameters(), lr=0.001)\n",
    "epochs = 5000\n",
    "x_train = torch.linspace(0, 1, 100).view(-1, 1)\n",
    "\n",
    "for epoch in range(epochs):\n",
    "    optimizer.zero_grad()\n",
    "    loss = loss_function(x_train)\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    if (epoch + 1) % 500 == 0:\n",
    "        print(f'Epoch {epoch+1}, Loss: {loss.item()}')\n",
    "\n",
    "# Predict the solution\n",
    "x_test = torch.linspace(0, 1, 100).view(-1, 1)\n",
    "N_pred = net(x_test).detach()\n",
    "u_pred = x_test * (1 - x_test) * N_pred\n",
    "\n",
    "# Convert to numpy for plotting\n",
    "x_test_np = x_test.numpy()\n",
    "u_pred_np = u_pred.numpy()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "ename": "ValueError",
     "evalue": "x, y, and format string must not be None",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[4], line 23\u001b[0m\n\u001b[0;32m     21\u001b[0m plt\u001b[38;5;241m.\u001b[39mfigure(figsize\u001b[38;5;241m=\u001b[39m(\u001b[38;5;241m8\u001b[39m, \u001b[38;5;241m6\u001b[39m))\n\u001b[0;32m     22\u001b[0m plt\u001b[38;5;241m.\u001b[39mplot(x_test_np, u_pred_np, label\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mPredicted Solution $u(x)$\u001b[39m\u001b[38;5;124m'\u001b[39m, color\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mb\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m---> 23\u001b[0m \u001b[43mplt\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mplot\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx_test_np\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mu_analytical_np\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mlabel\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mAnalytical Solution $u_\u001b[39;49m\u001b[38;5;124;43m{\u001b[39;49m\u001b[38;5;130;43;01m\\t\u001b[39;49;00m\u001b[38;5;124;43mext\u001b[39;49m\u001b[38;5;132;43;01m{analytical}\u001b[39;49;00m\u001b[38;5;124;43m}(x)$\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcolor\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mr\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mlinestyle\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43m--\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[0;32m     24\u001b[0m plt\u001b[38;5;241m.\u001b[39mxlabel(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m$x$\u001b[39m\u001b[38;5;124m'\u001b[39m, fontsize\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m14\u001b[39m)\n\u001b[0;32m     25\u001b[0m plt\u001b[38;5;241m.\u001b[39mylabel(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m$u(x)$\u001b[39m\u001b[38;5;124m'\u001b[39m, fontsize\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m14\u001b[39m)\n",
      "File \u001b[1;32mc:\\Users\\whn\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\matplotlib\\pyplot.py:2812\u001b[0m, in \u001b[0;36mplot\u001b[1;34m(scalex, scaley, data, *args, **kwargs)\u001b[0m\n\u001b[0;32m   2810\u001b[0m \u001b[38;5;129m@_copy_docstring_and_deprecators\u001b[39m(Axes\u001b[38;5;241m.\u001b[39mplot)\n\u001b[0;32m   2811\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mplot\u001b[39m(\u001b[38;5;241m*\u001b[39margs, scalex\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m, scaley\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m, data\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs):\n\u001b[1;32m-> 2812\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m gca()\u001b[38;5;241m.\u001b[39mplot(\n\u001b[0;32m   2813\u001b[0m         \u001b[38;5;241m*\u001b[39margs, scalex\u001b[38;5;241m=\u001b[39mscalex, scaley\u001b[38;5;241m=\u001b[39mscaley,\n\u001b[0;32m   2814\u001b[0m         \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m({\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mdata\u001b[39m\u001b[38;5;124m\"\u001b[39m: data} \u001b[38;5;28;01mif\u001b[39;00m data \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m \u001b[38;5;28;01melse\u001b[39;00m {}), \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n",
      "File \u001b[1;32mc:\\Users\\whn\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\matplotlib\\axes\\_axes.py:1688\u001b[0m, in \u001b[0;36mAxes.plot\u001b[1;34m(self, scalex, scaley, data, *args, **kwargs)\u001b[0m\n\u001b[0;32m   1445\u001b[0m \u001b[38;5;250m\u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[0;32m   1446\u001b[0m \u001b[38;5;124;03mPlot y versus x as lines and/or markers.\u001b[39;00m\n\u001b[0;32m   1447\u001b[0m \n\u001b[1;32m   (...)\u001b[0m\n\u001b[0;32m   1685\u001b[0m \u001b[38;5;124;03m(``'green'``) or hex strings (``'#008000'``).\u001b[39;00m\n\u001b[0;32m   1686\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[0;32m   1687\u001b[0m kwargs \u001b[38;5;241m=\u001b[39m cbook\u001b[38;5;241m.\u001b[39mnormalize_kwargs(kwargs, mlines\u001b[38;5;241m.\u001b[39mLine2D)\n\u001b[1;32m-> 1688\u001b[0m lines \u001b[38;5;241m=\u001b[39m [\u001b[38;5;241m*\u001b[39m\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_get_lines(\u001b[38;5;241m*\u001b[39margs, data\u001b[38;5;241m=\u001b[39mdata, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)]\n\u001b[0;32m   1689\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m line \u001b[38;5;129;01min\u001b[39;00m lines:\n\u001b[0;32m   1690\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39madd_line(line)\n",
      "File \u001b[1;32mc:\\Users\\whn\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\matplotlib\\axes\\_base.py:311\u001b[0m, in \u001b[0;36m_process_plot_var_args.__call__\u001b[1;34m(self, data, *args, **kwargs)\u001b[0m\n\u001b[0;32m    309\u001b[0m     this \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m args[\u001b[38;5;241m0\u001b[39m],\n\u001b[0;32m    310\u001b[0m     args \u001b[38;5;241m=\u001b[39m args[\u001b[38;5;241m1\u001b[39m:]\n\u001b[1;32m--> 311\u001b[0m \u001b[38;5;28;01myield from\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_plot_args\u001b[49m\u001b[43m(\u001b[49m\n\u001b[0;32m    312\u001b[0m \u001b[43m    \u001b[49m\u001b[43mthis\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mambiguous_fmt_datakey\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mambiguous_fmt_datakey\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[1;32mc:\\Users\\whn\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\matplotlib\\axes\\_base.py:465\u001b[0m, in \u001b[0;36m_process_plot_var_args._plot_args\u001b[1;34m(self, tup, kwargs, return_kwargs, ambiguous_fmt_datakey)\u001b[0m\n\u001b[0;32m    462\u001b[0m \u001b[38;5;66;03m# Don't allow any None value; these would be up-converted to one\u001b[39;00m\n\u001b[0;32m    463\u001b[0m \u001b[38;5;66;03m# element array of None which causes problems downstream.\u001b[39;00m\n\u001b[0;32m    464\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28many\u001b[39m(v \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m \u001b[38;5;28;01mfor\u001b[39;00m v \u001b[38;5;129;01min\u001b[39;00m tup):\n\u001b[1;32m--> 465\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mx, y, and format string must not be None\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m    467\u001b[0m kw \u001b[38;5;241m=\u001b[39m {}\n\u001b[0;32m    468\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m prop_name, val \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mzip\u001b[39m((\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlinestyle\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mmarker\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mcolor\u001b[39m\u001b[38;5;124m'\u001b[39m),\n\u001b[0;32m    469\u001b[0m                           (linestyle, marker, color)):\n",
      "\u001b[1;31mValueError\u001b[0m: x, y, and format string must not be None"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Plot the predicted solution\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(x_test_np, u_pred_np, label='Predicted Solution $u(x)$', color='b')\n",
    "plt.xlabel('$x$', fontsize=14)\n",
    "plt.ylabel('$u(x)$', fontsize=14)\n",
    "plt.title('Predicted Solution of the Poisson Equation', fontsize=16)\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "# Define the analytical solution (if known)\n",
    "def u_analytical(x):\n",
    "    return # Analytical solution expression\n",
    "\n",
    "# Compute the analytical solution\n",
    "u_analytical_np = u_analytical(x_test_np)\n",
    "\n",
    "# Plot both the predicted and analytical solutions\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(x_test_np, u_pred_np, label='Predicted Solution $u(x)$', color='b')\n",
    "plt.plot(x_test_np, u_analytical_np, label='Analytical Solution $u_{\\text{analytical}}(x)$', color='r', linestyle='--')\n",
    "plt.xlabel('$x$', fontsize=14)\n",
    "plt.ylabel('$u(x)$', fontsize=14)\n",
    "plt.title('Comparison of Predicted and Analytical Solutions', fontsize=16)\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
